Taylor's Frozen-in Hypothesis for Magnetohydrodynamic turbulence and Solar Wind

In hydrodynamics, Taylor's frozen-in hypothesis connects the wavenumber spectrum to the frequency spectrum of a time series measured in real space. In this paper, we generalize Taylor's hypothesis to magnetohydrodynamic turbulence. We analytically derive one-point two-time correlation functions for Els\"{a}sser variables whose Fourier transform yields the corresponding frequency spectra, $E^\pm(f)$. We show that $E^\pm(f) \propto |{\bf U}_0 \mp {\bf B}_0|^{2/3}$ in Kolmogorov-like model, and $E^\pm(f) \propto (B_0 |{\bf U}_0 \mp {\bf B}_0|)^{1/2}$ in Iroshnikov-Kraichnan model, where ${\bf U}_0, {\bf B}_0$ are the mean velocity and mean magnetic fields respectively.